Ohio State University Algebraic Geometry SeminarYear 20172018Time: Tuesdays 34pmLocation: MW 154 

TIME  SPEAKER  TITLE 
August 29
Tue, 3pm  Dave Anderson
(OSU) 
Determinantal formulas for degeneracy loci and BrillNoether theory 
September 5
Tue, 3pm  HsianHua Tseng
(OSU) 
On the quantum Krings of flag varieties of type A 
September 12
Tue, 3pm  Angelica Cueto
(OSU) 
Tropical geometry of genus 2 curves 
September 19
Tue, 3pm  Herb Clemens
(OSU) 
Elipticallyfibered CalabiYau (CY) threefolds and fourfolds in string theory 
October 3
Tue, 3pm  Seth Baldwin
(UNC) 
Positivity in Tequivariant Ktheory of flag varieties associated to KacMoody groups 
October 10
Tue, 3pm  TBA
() 
TBA 
October 17
Tue, 3pm  Roi Docampo
(Oklahoma) 
TBA 
October 24
Tue, 3pm  TBA
() 
TBA 
October 26
Thu, 4:10pm CH 240  Renzo Cavalieri
(Colorado State U.) 
Colloquium talk 
October 31
Tue, 3pm  Christin Bibby
(U. Michigan) 
TBA 
November 7
Tue, 3pm  Chris Manon
(U. Kentucky) 
TBA 
November 14
Tue, 3pm  Daniel Litt
(Columbia U.) 
TBA 
November 21
Tue, 3pm  TBA
() 
TBA 
November 28
Tue, 3pm  Jose Gonzalez
(UC Riverside) 
TBA 
December 5
Tue, 3pm  Matthew Satriano
(U. Waterloo) 
TBA 
January 9
Tue, 3pm  TBA
( ) 
TBA 
January 16
Tue, 3pm  TBA
() 
TBA 
January 23
Tue, 3pm  William Fulton*
(Michigan) 
(*to be confirmed) 
January 30
Tue, 3pm  TBA
() 
TBA 
February 6
Tue, 3pm  TBA
() 
TBA 
February 13
Tue, 3pm  TBA
() 
TBA 
February 20
Tue, 3pm  TBA
() 
TBA 
February 27
Tue, 3pm  TBA
() 
TBA 
March 6
Tue, 3pm  TBA
() 
TBA 
March 13
Tue, 3pm  (break)


March 20
Tue, 3pm  TBA
() 
TBA 
March 27
Tue, 3pm  TBA
() 
TBA 
April 3
Tue, 3pm  TBA
() 
TBA 
April 10
Tue, 3pm  TBA
() 
TBA 
April 1618
Tue, 4:10pm CH 240  Sergey Fomin
(U. Michigan) 
Zassenhaus Lecture Series 2018 
April 24
Tue, 3pm  TBA
() 
TBA 
(Anderson): Relations between degeneracy loci and divisors on curves go back over a hundred years: Giambelli's formula for the class of the locus where a matrix drops rank is a cornerstone of Schubert calculus; Brill and Noether's estimate for the dimension of the space of special divisors on a curve also comes from considerations of degeneracy loci. In this talk, I will describe work with Linda Chen and Nicola Tarasca which connects more recent developments in Schubert calculus with formulas by EisenbudHarris, Pirola, and ChanLopezPfluegerTeixidor for the genus of a BrillNoether curve.
(Tseng): The quantum Kring of a smooth projective variety X, introduced by Givental and YP Lee, is a deformation of the Grothendieck ring of coherent sheaves on X defined using holomorphic Euler characteristics on moduli spaces of stable maps to X (these are Ktheoretic version of GromovWitten invariants). In this talk we discuss some properties of the quantum Krings of X=Fl_{r+1}, the variety of complete flags in C^{r+1}, including:
(1) a presentation of the quantum Kring;
(2) finiteness of quantum product;
(3) canonical polynomial representatives of Schubert classes.
This is based on joint work in progress with David Anderson and Linda Chen.
(Cueto): In this talk, I will discuss the structure of tropical and nonArchimedean analytic genus 2 curves and their moduli from three perspectives:
(1) as 2to1 covers of P^{1} branched at 6 points;
(2) as solutions to the hyperelliptic equation y^{2}=f(x), where f has degree 5; and
(3) as metric graphs dual to genus 2 nodal algebraic curves over a valued field.
Our first description allows us to give an explicit combinatorial rule to characterize each such metric graph together with a harmonic map to a metric tree on 6 leaves, in terms of the valuations of 6 branch points in P^{1}. Even though the tropicalization of a plane hyperelliptic curve shows no genus, we provide explicit reembeddings of the input planar hyperelliptic curve that reveals the correct metric graphs.
From our third viewpoint, we consider the moduli space of abstract genus two tropical curves and translate the classical Igusa invariants characterizing isomorphism classes of genus two algebraic curves into the tropical realm. While these tropical Igusa functions do not yield coordinates on the tropical moduli space, we propose an alternative set of invariants that provides new length data. This is joint work with Hannah Markwig.
(Clemens): The talk will construct one example of the `equivalence' between an ellipticallyfibered CYthreefold endowed with a semistable E_{8} + E_{8} bundle and a semistable degeneration of an ellipticallyfibered CYfourfold. I will then loosely describe how this equivalence is used to `break' the SU(5)symmetry of grand unified theory (GUT) to the SU(3)xSU(2)xU(1)symmetry of what physicists call the Standard Model of the physics of our cosmos.
(Baldwin): The cohomology ring of flag varieties has long been known to exhibit positivity properties. One such property is that the structure constants of the Schubert basis with respect to the cup product are nonnegative. Brion (2002) and AndersonGriffethMiller (2011) have shown that positivity extends to Ktheory and Tequivariant Ktheory, respectively. In this talk I will discuss recent work (joint with Shrawan Kumar) which generalizes these results to the case of KacMoody groups.
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This page is maintained by Angie Cueto and Dave Anderson.